Identify the Zeros and Their Multiplicities f(x)=(x-9)(x+12)(x-24)

$f (x) = (x - 9) (x + 12) (x - 24)$

Step 1

Set $(x - 9) (x + 12) (x - 24)$ equal to $0$ .

$(x - 9) (x + 12) (x - 24) = 0$

Step 2

Solve for $x$ .

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 9 = 0$

$x + 12 = 0$

$x - 24 = 0$

Set $x - 9$ equal to $0$ and solve for $x$ .

Set $x - 9$ equal to $0$ .

$x - 9 = 0$

Add $9$ to both sides of the equation.

$x = 9$

Set $x + 12$ equal to $0$ and solve for $x$ .

Set $x + 12$ equal to $0$ .

$x + 12 = 0$

Subtract $12$ from both sides of the equation.

$x = - 12$

Set $x - 24$ equal to $0$ and solve for $x$ .

Set $x - 24$ equal to $0$ .

$x - 24 = 0$

Add $24$ to both sides of the equation.

$x = 24$

The final solution is all the values that make $(x - 9) (x + 12) (x - 24) = 0$ true. The multiplicity of a root is the number of times the root appears.

$x = 9$ (Multiplicity of $1$ )

$x = - 12$ (Multiplicity of $1$ )

$x = 24$ (Multiplicity of $1$ )

$x = 9$ (Multiplicity of $1$ )

$x = - 12$ (Multiplicity of $1$ )

$x = 24$ (Multiplicity of $1$ )

Step 3

Identify the Zeros and Their Multiplicities f(x)=(x-9)(x+12)(x-24)

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